Amy Winehouse's father claims there was one drug found in the singer's system when she died -- but he insists ... Amy had a prescription for it.

In an interview on Anderson Cooper's new talk show -- which airs Monday -- Mitch Winehouse admits Amy was taking a drug called Librium, which he describes as a drug for detoxing alcoholics.

According to Mitch, she had a prescription for it -- to help prevent seizures -- and she took one dose daily.

Unfortunately, Mitch says it didn't work like it was supposed to -- telling Anderson, he believes Amy died from an alcohol detox seizure ... and "there was nobody there to rescue her."

Mitch still insists there were ZERO illegal drugs in his daughter's system at the time of her death -- adding, "We really felt we were out of the woods. We saw the light at the end of the tunnel."